Investigation of students' problem-posing skills in the context of measuring length, area and volume

This study aims to examine seventh-grade students' problem-posing skills in the context of length, area, and volume measurement. The participants of the study were selected from seventh-grade students attending a public school in Turkey. Two different classes were included in the study; one was designated as the pilot group, while the other served as the main implementation group. The pilot group consisted of 11 students, including 3 girls and 8 boys. The main implementation group comprised 9 students selected through purposive sampling based on academic achievement criteria. The research was conducted using a qualitative research method, specifically adopting a case study design. As data collection tools, the Problem-Posing Interview Form and Problem-Posing Worksheets, developed by the researchers based on expert opinions, were utilized. A pilot implementation was carried out, and the clinical interviews were recorded on video. These recordings were transcribed to make them suitable for analysis. During the data analysis phase, content analysis was applied. As a result of the analysis, three main categories were identified: problem statement, mathematical language, and types of problem posing. According to the research findings, most of the problems constructed by students in the context of length, area, and volume measurement were limited to basic computational tasks, resembled practice exercises, and lacked a clear problem stem; thus, they were not accepted as mathematical problems. These types of questions were not considered mathematical problems because they did not require deep thinking and could be solved through simple procedures. On the other hand, when the mathematical problems created by students were examined, it was found that more than half of the students could construct solvable mathematical problems in structured, semi-structured, and free problem-posing situations. However, some of these problems contained various deficiencies, such as incomplete or incorrect information, inaccurate representations, and incorrect use of measurement units. Another notable finding of the study was that students showed a tendency to construct problems by modifying given figures or verbal expressions. During the problem-posing stages, students sometimes created problems similar to those provided, and at other times, they developed completely different problems. Especially in similar problem-posing cases, it was observed that students preserved the figures and contexts from the original problems to a large extent. In conclusion, this study offers significant implications for instructional processes aimed at improving students' problem-posing skills. It was understood that students need teacher guidance in order to better grasp the use of language and symbols in mathematical problems, represent information effectively, and manage problem-solving processes. In this context, providing students with more support during the problem-posing process will contribute to the more effective development of these skills.